An Introduction to Sound Waves in Synthesis

Complex sound wave

As electronic musicians, I think we have a sort of obligation to know how sound works, especially because we produce sound in a much more fundamental way than acoustic musicians. Sound is a very physical manifestation, and I think an insight into exactly how it works could be of use (or at the very least, inspiration) to you guys who use Ableton.

One disclaimer: I am not a physicist or acoustic specialist. If I get anything wrong, PLEASE correct me. :)

What is “sound”?

Sound is, put as simply as possible, vibrations in the air. Here’s a simplified version of how sound works, step by step:

  1. Little magnets in speakers vibrate depending on the wave that comes from the speaker cable.
  2. The speaker cone amplifies this vibration, and sends it into the air.
  3. These vibrations pass through the air.
  4. The same vibrations pass into your ear, and make your eardrum vibrate at the same rate.
  5. Oh no! It’s brostep! You suffer a stroke a wake up in the hospital, thankfully with no recollection of what you were listening to.

That’s how it works, in a nutshell. It’s kind of crazy to realize that sound is just a wave! Specifically, sound is a longitudinal wave, which means that instead of crests and troughs like you see on ocean waves, there are alternating parts of the wave that are scrunched up and spread out, like when you push a slinky:

Watch the above video, and imagine the hand is anything that makes sound. For example, when you clap, you create a difference in air pressure, which spreads out in all directions as a longitudinal wave. On the receiving end of the wave is your eardrum, and your brain somehow makes sense of this information (the explanation of this is beyond the scope of this tutorial, unfortunately, perhaps we’ll cover sound perception in a later article).

Basic Waves for Synthesis

The sine wave is the most basic type of wave, and I’m sure all of you familiar with synthesis know its shape. It’s a smooth curve, the most fundamental single frequency that can be produced. These are rarely (if ever) heard in nature, and almost always produced synthetically.

The sine wave has no overtones, just a single fundamental frequency. This can be seen in Ableton’s frequency spectrum. Open a new Operator synth, and click on the “Oscillator” switch under the ADSR viewport. You’ll see a graph-looking thing.

Sine wave

This represents each harmonic (or “overtone”) of the sound. The x-axis represents frequency (pitch), and the y-axis represents amplitude (loudness). Harmonics are represented by each bar on the graph. A harmonic is a multiple of the fundamental frequency (the first bar on the left). So, when your fundamental frequency is 200 Hz, your harmonics are 400 Hz, 600 Hz, 800 Hz, etc. (See G’s comment about the relationship between harmonics and octaves)

This is kind of a hard concept to grasp, but really important. You’ll understand it better when we look at sawtooth waves.

Saw wave

As you can see from the above frequency spectrum of a saw wave, each harmonic is present, but with decreasing amplitude. This is why saw waves sound fuller than sine waves — they are rich in overtones.

And a square wave is the same as a saw wave, but skips every other harmonic:

Square wave

Each “harmonic”, though, is a sine wave. So when you play a 200 Hz sawtooth wave, you’re really playing a 200 Hz sine wave plus a 400 Hz sine wave at a slightly lower volume, PLUS a 600 Hz sine wave at an even slightly lower volume, and so on. This addition of harmonics is what gives sine, saw, triangle, and square waves their individual sound qualities, because when you add one wave to another, it changes the shape of the wave.

Try adding sine waves together at this website. Type in, from left to right, 100, 100, 0, 200, 50, 0, and uncheck “Sum”. This will show you the two individual waves. After checking “Sum”, you can see what happens when the two waves are combined.

Wave interference

Notice how the source waves and the resulting complex wave are periodic — they repeat in a regular pattern. This is what happens when two waves are harmonically related (whole number multiples of each other) to the fundamental (or lowest) frequency. When two waves aren’t multiples, you get noise (see below).

In Operator, you can put together your own waves by drawing whatever harmonics you want on the Oscillator windows. As you do this, you can see the shape of the wave change below. This is what’s happening — sine waves are getting added to one another, with different results.

You can also change the phase (the x-axis offset of the wave) in Operator, as well as add multiple oscillators to each other in a process called FM synthesis, which we will cover in a later tutorial.

Noise

Just a quick note about “noise”, which I’m sure you’re all familiar with if you’ve ever listened to the radio:

The most common type of noise is white noise, which is where that every frequency in a given bandwidth has equal magnitude. This creates a sonic mash that is quite useful in creating atonal sounds such as snare drums and hi-hats. Noise can also be an effective addition to other oscillators in FM synthesis.

But there are other types of noise that result when certain frequencies along the spectrum have lower or higher relative amplitudes. As expected, Wikipedia has a list of all the colors of noise for those interested.

That’s all for now

We could go deeper, but I just wanted to cover the basics in this article. Hopefully I’ve cleared up some of the obvious and fundamental things about sound that you’ve been avoiding learning about. Sometimes it’s important to take a step back, stop making music, and learn a bit more about the physical thing we make every day. If I’ve done my job right, you’ll approach your synthesizer from now on with a much richer appreciation of sound. :)

8 comments on “An Introduction to Sound Waves in Synthesis

  1. “These are rarely (if ever) heard in nature, and almost always produced organically.”

    I think you mean synthetically if its not in nature.

  2. “In music, a whole-number multiple of the fundamental frequency is an octave.”

    When ever a given frequency is doubled, it rises an octave. For example, when the frequency of an A note at 440 Hz is doubled (i.e. multiplied by two), to 880 Hz, the resulting tone is one octave higher. To get another octave above that, you again double the frequency and arrive at 1760 Hz. That’s the original frequency multiplied by four.

    Naturally it also follows that, even though all of the frequencies in such an octave series are whole-number multiples of the fundamental (the multipliers being powers of two), most whole-number multiples of the fundamental don’t represent an octave ;)

  3. What. the. hell… is brostep? I thought dubstep was on its way out.

    Never thought of the atonal sounds, is that why snare and hi hats fit in nearly every song without sounding off key?

    Also would love to see how the area where you draw in the harmonics correlates to the shape of the wave. For example, why does the single harmonic make that smooth Sine wave?

    • Steven Campbell on said:

      Brostep is your worst nightmare.

      Each harmonic on its own is a sine wave — the purest and simplest sound. So if you draw just one harmonic, you will always see a sine wave. When you start adding harmonics together, that’s when the shape starts to change. See this Wikipedia article for more information.

      And this video should be especially helpful in describing how waves are added together.

    • Ah, I guess you addressed that bit above with the combination of sines. I’ll check those links out now. Thanks!

  4. David D.L. on said:

    Awesome article! This blog is most likely the best Ableton related site out there!

    On a sidenote, I fully agree…Brostep is indeed our worst nightmare, especially when you live in that a city whose entire electronic music scene is either cheesy knock-offs of Richie Hawtin…or ear-haemorrhage-inducing brostep…I will now curl-up in a ball and cry…:)

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